Hereditarily Finite

Some articles on hereditarily finite, finite, hereditarily:

Hereditarily Finite Set
... In mathematics and set theory, hereditarily finite sets are defined recursively as finite sets consisting of 0 or more hereditarily finite sets ...
Hereditarily Finite Set - Formal Definition
... A recursive definition of a hereditarily finite set goes as follows Base case The empty set is a hereditarily finite set ... Recursion rule If a1...ak are hereditarily finite, then so is {a1...ak} ... The set of all hereditarily finite sets is denoted Vω ...
Hereditary Property - In Set Theory
... A couple of notions are defined analogously A hereditarily finite set is defined as a finite set consisting of zero or more hereditarily finite sets ... Equivalently, a set is hereditarily finite if and only if its transitive closure is finite ... A hereditarily countable set is a countable set of hereditarily countable sets ...

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